Numerical implementation of some reweighted path integral methods

The reweighted random series techniques provide finite-dimensional approximations to the quantum density matrix of a physical system that have fast asymptotic convergence. We study two special reweighted techniques that are based upon the Levy-Ciesielski and Wiener-Fourier series, respectively. In agreement with the theoretical predictions, we demonstrate by numerical examples that the asymptotic convergence of the two reweighted methods is cubic for smooth enough potentials. For each reweighted technique, we propose some minimalist quadrature techniques for the computation of the path averages. These quadrature techniques are designed to preserve the asymptotic convergence of the original methods.Comment: 15 pages, 10 figures, submitted to JC

Participation in college sports and protection from sexual victimization

Some sociologists have argued that sport is a male-dominated institution and sexist culture in which female athletes experience various forms of discrimination, including sexual harassment from coaches and male athletes. Some research does indicate that female athletes suffer higher rates of sexual victimization from authority figures in sport than their nonathletic counterparts in education and the workplace. In contrast, researchers have also speculated that athletic participation can protect female athletes from sexual victimization through a variety of social-psychological mechanisms such as team membership, physical strength, and self-confidence. This paper reports on the first descriptive analysis to test the “sport protection hypothesis” among both female and male athletes, using cross-tabulation secondary analyses of data from the National College Health Risk Behavior Survey, conducted in 1995 by the U.S. Centers for Disease Control and Prevention (N=4814). USA college students of traditional undergraduate age (aged 18-24) were included in the sample (N=2903). Some limited support for the protection hypothesis was found, and student athletes were significantly less likely to report sexual victimization during their late high school and early college years than their nonathletic counterparts. A gender gap in the pattern of sexual victimization also appeared between males and females across all student age groups, with females experiencing more sexual victimization than males. However, no significant gender gap was found among athletes. The results are discussed in relation to previous studies of campus athletes and to college prevention policy

Energy estimators for random series path-integral methods

We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method) and the direct (H-method) energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first and second order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires k + 1 times more calls to the potential, where k is the order of the difference scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster demonstrate that a second order central-difference scheme should suffice for most applications.Comment: 11 pages, 4 figure

Hydration of Kr(aq) in dilute and concentrated solutions

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Kr\"{u}ger, \emph{et al.}, yield a modestly attractive osmotic second virial coefficient, $B_2\approx -60~\mathrm{cm}^3$/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both.Comment: 6 pages, 7 figures. Revision follows the extrapolation procedure of Refs. 33 and 34 which works nicely. The thermodynamic results are now clearly consistent. The $k \rightarrow 0$ extrapolation of the Fourier transform was not was satisfactor

Taming the rugged landscape: production, reordering, and stabilization of selected cluster inherent structures in the X_(13-n)Y_n system

We present studies of the potential energy landscape of selected binary Lennard-Jones thirteen atom clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. We analyze the energy landscapes of the studied systems using disconnectivity graphs. The required inherent structures and transition states for the construction of disconnectivity graphs are found by combination of conjugate gradient and eigenvector-following methods. We show that it is possible to controllably induce new structures as well as reorder and stabilize existing structures that are characteristic of higher-lying minima. Moreover, it is shown that the selected structures can have experimentally relevant lifetimes.Comment: 12 pages, 14 figures, submitted to J. Chem. Phys. Reasons for replacing a paper: figures 2, 3, 7 and 11 did not show up correctl

Phase changes in selected Lennard-Jones X_{13-n}Y_n clusters

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X_{13-n}Y_n (where n=1,2,3) are presented. The total energy, heat capacity and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated.Comment: 14 pages, 13 figures. submitted to J. Chem. Phy

Stem Cell Transplantation As A Dynamical System: Are Clinical Outcomes Deterministic?

Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However the clinical course following SCT appears to demonstrate many characteristics of dynamical systems, especially when outcomes are considered in the context of immune reconstitution. Dynamical systems tend to evolve over time according to mathematically determined rules. Characteristically, the future states of the system are predicated on the states preceding them, and there is sensitivity to initial conditions. In SCT, the interaction between donor T cells and the recipient may be considered as such a system in which, graft source, conditioning and early immunosuppression profoundly influence immune reconstitution over time. This eventually determines clinical outcomes, either the emergence of tolerance or the development of graft versus host disease. In this paper parallels between SCT and dynamical systems are explored and a conceptual framework for developing mathematical models to understand disparate transplant outcomes is proposed.Comment: 23 pages, 4 figures. Updated version with additional data, 2 new figures and editorial revisions. New authors adde

Taming the rugged energy landscape: Techniques for the production, reordering, and stabilization of selected cluster inherent structures

We report our studies of the potential energy surface (PES) of selected binary Lennard-Jones clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. Inherent structures and transition states are found by combination of conjugate-gradient and eigenvector-following methods while the topography of the PES is mapped with the help of a disconnectivity analysis. We show that we can controllably induce new structures as well as reorder and stabilize existing structures that are characteristic of higher-lying minima.Comment: 9 pages, 9 figures, accepted for publication in J. Chem. Phy